Why is the validation performance better than the training performance?
Assuming you pass through the entire validation dataset, this can't be due to shuffling since you still compute the loss/accuracy over the entire dataset, so order does not really matter here. It is more likely that you have a significantly smaller or less representative validation dataset, e.g., distribution of the validation dataset can be skewed towards classes where your model performs better.
What do you mean exactly by improving the situation? Having a better validation accuracy is not necessarily bad. In any case, if you decrease the effect of regularization, e.g., lowering weight decay, training accuracy might go up but your model might generalize worse, i.e.,  you might get a lower validation accuracy.
No, the goal of training is never to maximize training accuracy. You can trivially do so by just memorizing the training dataset. In short, the goal of training is to get good generalization and as long as you get a satisfactory validation accuracy, it is likely that this has happened to some degree (assuming you have a good validation dataset of course).